Locally free sheaf: Difference between revisions
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#redirect [[Coherent sheaf]] |
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In [[sheaf theory]], a field of mathematics, a sheaf of <math>\mathcal{O} _X</math>-modules <math>\mathcal{F}</math> on a [[ringed space]] <math>X</math> is called ''locally free'' if for each point <math>p\in X</math>, there is an [[topological space|open]] [[neighborhood (mathematics)| neighborhood]] <math>U</math> of <math>p</math> such that <math>\mathcal{F}| _U</math> is [[free module|free]] as an <math>\mathcal{O} _X| _U</math>-module, or equivalently, <math>\mathcal{F}_p</math>, the [[Stalk of a sheaf|stalk]] of <math>\mathcal{F}</math> at <math>p</math>, is free as a <math>(\mathcal{O} _X)_p</math>-module. If <math>\mathcal{F}_p</math> is of finite rank <math>n</math>, then <math>\mathcal{F}</math> is said to be of rank <math>n.</math> |
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==See also== |
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* [[Swan's theorem]] |
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==References== |
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*Section 0.5.4 of {{EGA|book=I}} |
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==External links== |
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*{{planetmath|id=4618|title=Locally free}} |
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[[Category:Algebraic geometry]] |
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[[Category:Sheaf theory]] |
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[[he:אלומה חופשית באופן מקומי]] |
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Latest revision as of 13:35, 16 July 2023
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